The purpose of this study is to introduce the possibility that there is a difference between the standard calculated beta and a conditional beta based upon the direction of the market. This article is meant to be more of an introduction to a series of articles related to the idea of a conditional beta, so please be patient, and feel free to offer any comments, advice, or constructive criticism. I also have a few next steps in the works, but if anyone has any more ideas on where to take this, please let me know.

**Initial Observation and Hypothesis**

I was recently setting up an equity trade and was running the calculations to make the trade beta neutral. One of the positions is a stock which is quite volatile. Most interestingly, I noticed that when the market was up, this stock usually performed in line with the standard beta. However, if the market was down, the stock usually performed worse than expected, based on the same beta calculations. Of note, there were no significant market or company events that tended to skew my observation.

Granted, the return for any stock is comprised of systemic (beta or market) risk, idiosyncratic (individual company) risk, with some error in there just for completeness. So, I completely understand that this pattern I was noting may be due to other issues. However, when I started to dig into the data, I was surprised by what I found.

**Method**

In order to gather the appropriate data, I used the free Excel Addin located here. If you don’t want to register with the Yahoo! Group, you can find a download link at** **my site. As well, a more technical write up as well as a download to the latest spreadsheet can be found at my web site here. It may be down at the moment as I am currently revamping my site, but will be up within the week.

Basically, I gathered 5 years of daily data for a selection of market ETFs. Once you input the ticker symbol you are interested in, the sheet will automatically calculate the Beta and R-Square for each of the market ETFs. To get the data for the conditional beta, you click the “Update Data” button. This will engage a few embedded macros which will do an advanced filter for each of the ETFs, sorting the up days for the indexes from the down days. Once the data is separated into the index up days vs. down days, it is simple to find the beta and R-square for each of the respective data sets.

**Output**

For this example, I have used AMD (NASDAQ:AMD), just because it is a security that I know is not symmetrical. Once you have typed in the ticker and updated the data using the macro-enabled button, you will first see the data table for the beta calculations.

**AMD Beta Table: Comparing AMD betas to different Index ETFs ***[click images to enlarge]*

Notice that the R-Square for both QQQ and IWM are pretty similar for the traditional beta (top two rows). What I want to point out is the "Beta Down" of QQQ is 1.7, compared to its traditional beta of 1.38. As you can imagine, if you used a traditional beta calculation for a market neutral trade using AMD, you may find yourself grossly over/underexposed, depending on what side of the trade AMD is on, as well as the market direction.

The next thing you will notice are the scatterplot graphs showing the traditional beta calculation, as well as the conditional beta calculations (below).

**AMD Traditional Beta Scatterplot**

**AMD Beta Up Scatterplot: Quite a dispersion**

**AMD Beta Down Scatterplot: Scale is an issue**

When I look at these charts and others like it, it reminds me of how imprecise the beta number really is. Even if broken into smaller pieces, the data shows massive amounts of dispersion.

Finally, I added a couple of graphs for my own curiosity, namely a daily return histogram and a 12-month trailing beta study.

**AMD vs QQQ Daily Return Histogram: Just for fun**

In and unto itself, I find the daily histogram meaningless, and would prefer a weekly or monthly histogram. I just haven't gotten that far.

**AMD Rolling 12-Month Beta Study: Looking at trends**

I created this analysis because I wanted to be able to see how different securities reacted based on the direction of the market. Also, when calculating position sizes for beta-neutral trades, it is extremely helpful to know how each security will act depending on your view of market direction.

Now the real question is, how can this deeper dive into the beta of a company be useful?

For now, I am going to leave it as purely informational. I am not a "quant", and have only the basic statistical and mathamatical training afforded to me by my undergrad in Corporate Finance, my MBA at UNC, and the CFA level I exam. I personally use it just as a check up before I finalize a market-neutral trade. In many cases, the standard calculated beta is just fine, and 10 times easier to implement. However, in some cases, like AMD, a standard calculation is not adequate.

My next post will be my methods and findings on how to analyze the conditional beta information in order to integrate the data into my market neutral position calculator.

In the meantime, I look forward to your comments and feedback.

**Warning/Disclaimer:**

When using this data, please remember that the R-square values are not additive in nature, and that the conditional beta studies will not add up to the whole beta. As well, I have yet to see where the conditional beta studies have a higher R-square than the whole beta.

The R-square is strictly to use as an indicator of goodness of fit, its bounds being 0 (no fit) and 1 (perfect fit). So, make sure that the only time you are comparing two R-squares are

- When initially selecting an index: the higher the R-squared, the better the fit.
- When you are comparing the conditional betas to the whole beta: if a conditional beta has an R-squared that is reasonably close to the whole beta, it may be useful.

**Disclosure: **I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.